/**
 * 37. 解数独
 * https://leetcode.cn/problems/sudoku-solver/description/
 */
class Solution {
    boolean row[][];
    boolean col[][];
    boolean grid[][][];
    public void solveSudoku(char[][] board) {
        row = new boolean[9][10];
        col = new boolean[9][10];
        grid = new boolean[3][3][10];

        //初始化
        for(int i = 0; i < 9; i++) {
            for(int j = 0; j < 9; j++) {
                if(board[i][j] != '.') {
                    int num = board[i][j] - '0';
                    row[i][num] = col[j][num] = grid[i / 3][j / 3][num] = true;
                }
            }
        }
        dfs(board);
    }

    public boolean dfs(char[][] board) {
        for(int i = 0; i < 9; i++) {
            for(int j = 0; j < 9; j++) {
                if(board[i][j] == '.') {
                    for(int num = 1; num <= 9; num++) {
                        //剪枝
                        if(!row[i][num] && !col[j][num] && !grid[i / 3][j / 3][num]) {
                            board[i][j] = (char)('0' + num);
                            row[i][num] = col[j][num] = grid[i / 3][j / 3][num] = true;
                            if(dfs(board) == true) return true; //重点理解
                            //回溯
                            board[i][j] = '.';
                            row[i][num] = col[j][num] = grid[i / 3][j / 3][num] = false;
                        }
                    }
                    return false;//重点理解
                }
            }
        }
        return true;//重点理解
    }
}